Publisher: GSA Journal: GEOL: Geology Article ID: G Pacific plate deformation from horizontal thermal contraction

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1 1 Pacific plate deformation from horizontal thermal contraction 2 Corné Kreemer 1 and Richard G. Gordon 2 1 Nevada Bureau of Mines and Geology, and Seismological Laboratory, University of Nevada, 3 4 Reno, 1664 N. Virginia Street, Reno, Nevada , USA 2 Department of Earth Science, Rice University, MS 126, 6100 Main Street, Houston, Texas , USA 7 ABSTRACT 8 The central approximation of plate tectonics is that the plates are rigid, which gives the 9 theory its rigor and predictive power. Space geodetic measurements are consistent with the 10 rigidity of stable plate interiors, but some failures of plate-circuit closure, in particular of oceanic 11 plates, indicate that plates may be measurably non-rigid. We explore the hypothesis that 12 horizontal thermal contraction causes deformation of oceanic plates. Here we show significant 13 expected displacement fields due to thermal contraction for the Pacific plate based on a 14 previously proposed relationship between sea-floor age and strain rate and on two end-member 15 assumptions on how strain compatibility is enforced. The predicted maximum 2.2 mm/yr south- 16 eastward motion of the north-eastern part of the plate relative to the Pacific-Antarctic Rise may 17 contribute to a large part of the non-closure of the Pacific-North America plate motion circuit. 18 Our predicted displacement rates cannot (yet) be confirmed by current space-geodetic data and 19 will require seafloor geodesy with 1 mm/yr accuracy. The spatial distribution of predicted 20 moment rate agrees reasonably well with that of intraplate earthquakes epicenters, similar to 21 what is observed for plate boundary zones. Our results suggest that plate-scale horizontal thermal 22 contraction is significant and that it may be partly released seismically. 23 INTRODUCTION Page 1 of 14

2 24 Publisher: GSA Plate tectonics has transformed our view of how our planet works. The central 25 assumption or approximation of plate tectonics is that the plates are rigid. The assumption of 26 plate rigidity is what gives plate tectonics its rigor and predictive power. There are two main 27 quantitative tests of plate rigidity: plate-circuit closure and space geodetic measurements. The 28 hypothesis of plate rigidity has survived many critical tests (e.g., DeMets et al., 1990; Argus and 29 Gordon, 1996; Dixon et al., 1996; Beavan et al., 2002). 30 Nonetheless, there is mounting evidence that tectonic plates, in particular oceanic plates, 31 are not rigid. For example, DeMets et al. (2010) find the largest misfit in the 3-plate circuit (i.e., 32 inverting data only along the 3 mutual boundaries of those 3 plates) occurs for the Pacific-Nazca- 33 Cocos circuit, namely 14 ± 5 mm/yr (95% confidence limit). Another important circuit that fails 34 closure is the 4-plate Pacific-Antarctica-Nubia-North America circuit (i.e., using data only along 35 the Pacific-Antarctica boundary, the Antarctica-Nubia boundary, and the Nubia-North 36 America boundary) used in plate reconstructions to estimate motion between the Pacific and 37 North American plates. The sum of relative plate motions can be compared with geodetic 38 estimates of Pacific-North America motion. This circuit fails closure with a misfit of 5 ± 3 39 mm/yr (DeMets et al., 2010). 40 There are several possible explanations for the non-closure of plate circuits; e.g., motion 41 of tectonic plates over the non-spherical Earth causes deformation of the plates (McKenzie, ; Turcotte, 1974). The explanation we explore here, however, is that some or all of the 43 circuit misfits are caused by horizontal thermal contraction of the lithosphere. That such 44 contraction occurs is assumed in the work of many who have studied the thermal evolution of the 45 lithosphere and thermo-elastic stresses (e.g., Parmentier and Haxby, 1986; Sandwell and Fialko, ). The focus in most of these prior studies has been the difference in horizontal contraction Page 2 of 14

3 47 between the upper and lower portions of the competent oceanic lithosphere (i.e., the lithosphere 48 above the brittle-plastic transition (BPT)) and the bending moments applied to the lithosphere 49 and the resulting flexure. Here we investigate the effect of vertically averaged horizontal thermal 50 contraction in young oceanic lithosphere on plate-scale deformation by modeling the associated 51 strain rate field. We focus on the Pacific plate. 52 HORIZONTAL THERMAL CONTRACTION 53 Kumar and Gordon (2009) presented the assumptions and methods used to determine the 54 strain rate in cooling lithosphere due to thermal contraction. In one dimension, infinitesimal 55 strain rate (ε()) due to a cooling rate ( T / t ) is =α ( l T / t )ε where T is temperature, t is 56 time, and α l is the linear coefficient of thermal expansion, which has a value of 10 5 K -1. We 57 assume that the horizontal contraction of oceanic lithosphere will be a response to thermal stress 58 averaged from the surface of the lithosphere down to the base of the competent lithosphere. We 59 assume that stresses are relaxed by solid-state flow below the BPT. Kumar and Gordon (2009) 60 showed that the depth-averaged cooling rate for a column of competent lithosphere to equal 61 T m [exp( A 2 ) 1]/2At π where A=erf 1 (T l /T m ), T l is the temperature of the isotherm 62 bounding the base of the competent lithosphere, and T m is the initial temperature in a half-space 63 cooling model (Turcotte and Oxburgh, 1967). Estimates of T m range from 1300 C to 1350 C 64 (Hillier and Watts, 2005; McKenzie et al., 2005). Following Kumar and Gordon (2009), we 65 choose the lower value for T m as is it leads to lower contraction rates than the alternative and 66 thus we consider it to the be the more conservative option. McKenzie et al. (2005) and Wiens 67 and Stein (1983) showed that the limiting depth of earthquakes approximately follows 600 C. 68 Martinod and Molnar (1995) assumed the BPT to occur at a depth 20% greater than that of the Page 3 of 14

4 69 limiting depth of earthquakes. We therefore set T l to 700 C. This temperature also gives the 70 best fit to the amplitude of geoid anomalies due to thermal stresses on profiles across fracture 71 zones (Parmentier and Haxby, 1986). With the chosen values for T l, T m, and α l, we find 72 ε /t. We do not consider alternative cooling models as those differ only from 73 the half-space cooling model for ages >70 Ma where the expected strain rates will be an order- 74 of-magnitude lower than in the youngest lithosphere. We take t = t +t 0 with t being the age of 75 the lithosphere and t 0 being a parameter that accounts for the nonzero thickness of lithosphere 76 along the axis of mid-ocean ridge segments. We assume t 0 equals 0.1 Ma, which corresponds to 77 a zero-age lithospheric thickness of 2 km (Kumar and Gordon, 2009). Kumar and Gordon 78 (2009) discussed the strain rates and displacement rates expected from horizontal thermal 79 contraction in a general way. Here we make explicit predictions for the Pacific plate. 80 RESULTS 81 We use the sea-floor age model (v. 3.6) of Müller et al. (1997) to estimate strain rates in 82 grid cells 0.2 by 0.25 in longitude and latitude, respectively. Because of the 1/t dependency of 83 strain rate, we estimate the average age in each grid cell as the inverse average of the reciprocal 84 age values in that cell. The total model of 197,343 cells spans the entire Pacific plate, with its 85 boundaries defined by ridge-transform segments in the east and south (C. DeMets, pers. comm., ) and predominantly subduction zone trenches in the west and north (Bird, 2003). We set 87 the age of areas with unknown age to 200 Ma. 88 We apply the method of Haines and Holt (1993) to determine a continuous model of 89 strain rates and associated velocities that best fits the expected age-based strain rate. For each 90 grid cell the strain rates, and corresponding a priori covariance matrix, are set according to bi- Page 4 of 14

5 91 axial, age-derived, shortening both parallel and perpendicular to the local age gradient. If we 92 simply allowed the cells to shrink without enforcing strain compatibility, gaps would open up 93 everywhere in our model with the largest gaps opening up in the youngest lithosphere. If we 94 forced all the gaps to close in young lithosphere, the result would be overlap in old lithosphere. 95 Thus a sensible compromise is required for balancing extensional strains and contractional 96 strains while enforcing strain compatibility along the boundaries of all the cells. 97 We consider two end-member cases in which the continuous model should best fit the 98 expected strain rates. In Model 1, the a priori covariance matrix is set such that the modeled 99 continuous area strain rate amplitudes best match the expected values for each grid cell, but the 100 shortening rates parallel and perpendicular to the age gradient are not required to be equal. In 101 Model 2, the a priori covariance matrix is set such that the model continuous tensor field best 102 satisfies the expectation of isotropic shortening, but the area strain rates do not fit as well as in 103 Model 1. In effect, the difference between the models is on how we set the a priori correlation 104 between the two strain axes (0 for Model 1 and 1 for Model 2). The strain rates for Models 1 and 1052 are broadly similar but differ in detail (Fig. 1A and B, respectively). The deviations from the 106 level of expected area strain rates and the isotropy of shortening are shown in the Electronic 107 Supplement. For both models, the straining of the Pacific plate is dominated by horizontal 108 thermal contraction but also include regions of extensional strain evidently required by strain 109 compatibility and the other assumptions of our models (Figs. 1A and 1B). The regions of 110 extension tend to be in older lithosphere and might be much smaller or disappear altogether if we 111 assumed that lithospheric strength increased with age. 112 The associated velocity field results from the spatial integration of strain rates across the 113 Pacific lithosphere. In young lithosphere the ridge-parallel component of the velocity field is Page 5 of 14

6 114 potentially larger than the ridge-normal component, because there is more lithosphere with 115 relatively large strain rate across which to integrate. The ridge-parallel component is, however, 116 controlled by offsets of ridge segments by transform faults, limiting the velocity. For Model 2, 117 Figure 1C shows the velocity field in a reference frame that minimizes the predicted velocities at 118 a set of GPS stations in old Pacific lithosphere and Figure 1D shows the velocity field in a 119 reference frame that minimizes the velocities of points on the 0.78 Ma isochron (Müller et al., ) along the Pacific-Antarctic Ridge. The velocity fields for Model 1 are shown in the GSA 121 Data Repository and are fairly similar to those for Model 2. To test whether the thermal 122 contraction can be observed geodetically, we also analyze data from available continuous GPS 123 stations (see GSA Data Repository). Residual horizontal GPS velocities (after subtraction of a 124 rigid-body rotation) are shown in Figure 1C. 125 DISCUSSION 126 Most GPS residual velocities differ insignificantly from zero at the 95% confidence level 127 after we solve for and remove a rigid-body rotation (Fig. 1C). The reduced χ 2 is 2.4. We did 128 not use the velocity for the stations at Guadalupe and Chatham Islands to calculate the rigid-body 129 rotation. The station on Guadalupe Island is one of the few sites that has a considerable, but 130 insignificant (95% C.L.), motion of 1.2 ± 1.3 mm/yr toward S25 E. Previous estimates for this 131 station were larger and significant (Plattner et al., 2007; Argus et al., 2010). Either way, that 132 station s motion cannot be explained by thermal contraction, which is mm/yr toward SW 133 at this location. For the area containing the Chatham Rise and Campbell Plateau, SE of New 134 Zealand, our model predicts the largest velocities relative to the GPS locations on the old 135 lithosphere. The 0.6 mm/yr eastward and 0.6 mm/yr southward motion for stations CHAT and 136 CHTI on Chatham Island are roughly consistent with our predictions, but with only the former Page 6 of 14

7 137 observation being significant. At Campbell Island (i.e., southwestern most Pacific island) we 138 predict mm/yr to the SE, inconsistent with a campaign velocity there of 3.7 mm/yr 139 toward the NW (Beavan et al., 2002). If we transform that study s velocity field onto ours, 140 however, the observed motion of Campbell Island becomes insignificant. A real test of whether 141 our prediction is correct requires the installation of a CGPS station on Campbell Island (and 142 other nearby islands) or seafloor geodesy with 1 mm/yr accuracy. 143 We also present the predicted velocity field relative to the 0.78 Ma isochron along the 144 Pacific-Antarctic Ridge (Fig. 1D) to see how thermal contraction of the Pacific plate modifies 145 the results found assuming plate rigidity in the Pacific-Antarctic-Nubia-North America plate 146 motion circuit. In this approximate reference frame, places offshore Baja California move (Model 1) to 2.2 (Model 2) mm/yr toward the SE. The GPS station at Guadalupe Island could be 148 used to test for that motion, but only if we had several GPS stations on the southernmost Pacific 149 plate to provide a geodetic reference. Unfortunately, there are nearly no islands there. Although 150 the up-to-2.2 mm/yr motion off western North America may help to explain the failure to close 151 the Pacific-Antarctic-Nubia-North America circuit by 5 ± 3 mm/yr (DeMets et al., 2010), the 152 thermal contraction in the Antarctic, Nubia, and North American plates needs to be modeled to 153 address the problem fully. In any case, it is unlikely that thermal contraction can entirely explain 154 a non-closure as large as the 14 ± 5 mm/yr observed for the Pacific-Nazca-Cocos circuit 155 (DeMets et al., 2010), suggesting that additional deformation processes are involved in that 156 three-plate circuit. 157 Is there other evidence that thermal contraction exists and controls the Pacific plate s 158 intraplate strain rate field? To address this, we convert predicted strain rates to tectonic 159 moment rates (which are proportional to strain rate times volume) and compare them with Page 7 of 14

8 160 earthquake distributions. The number of events should be proportional to the tectonic moment 161 rate if seismicity follows a Gutenberg-Richter distribution and the b-value and maximum 162 expected moment are the same everywhere (e.g., Molnar, 1979). We use a catalog of intraplate events and explain the catalog in the GSA Data Repository. 164 We order our model grid cells from oldest to youngest age and count the cumulative 165 number of events, until 5 Ma (we exclude younger lithosphere to avoid possibly counting ridge- 166 transform events as being intraplate). The normalized graph is shown in Figure 2A. The same 167 figure also shows for Model 1 and 2 the normalized cumulative moment rate (M 0 ) for the same 168 cell ordering. For the strain-to-moment conversion we assume that the seismogenic thickness 169 follows the 700ºC isotherm. We also calculate the moment rates for alternative conversions in 170 which the maximum seismogenic thickness is limited to 40 km. Our results show that all curves 171 have the same concave-up shape. A general decrease in seismicity with age was already 172 observed by Wiens and Stein (1983) and the similarity in the curves suggest that horizontal 173 thermal contraction provides a first-order control on this decrease. Because of the limited number 174 of available earthquakes, it is not possible to prefer one particular moment rate model over 175 another. From Figure 1A it is clear that there is a change in seismicity rate around 30 Ma. If a 176 correlation between earthquake numbers and M 0 exists, we would expect it to be most obvious in 177 the younger lithosphere. We therefore also show a similar comparison but only for ages between 1785 and 30 Ma (Fig. 2B), which contains 21 events. For this case both cumulative earthquakes and 179 predicted M 0 form a similar linear relationship with age. 180 The correlation we observe between tectonic moment rate and number of events has also 181 been found for most subduction zones and continental deformation zones (Kreemer et al., 2002; 182 Kagan, 1999). These correlations do not, however, indicate the possibility that some, but not all, Page 8 of 14

9 183 of the tectonic moment could be released aseismically. If all tectonic moment is released 184 seismically, an unrealistically high maximum magnitude of >9 is needed to explain the 185 earthquake rate and observed b-value (Okal and Sweet, 2007); thus most of the thermal strain 186 rate in the Pacific is probably released aseismically. Moreover, it is expected that the moment 187 release mainly reflects the differential rates of cooling with depth (Wessel, 1992) and not the 188 vertically averaged cooling we consider here. 189 CONCLUSIONS 190 Strain rates from horizontal thermal contraction are much smaller than those occurring in 191 narrow plate boundaries and generally below the level of direct detection with GPS 192 measurements. When integrated across the plate away from the Pacific-Antarctic Ridge, 193 however, velocities can become 2.2 mm/yr off the coast of western North America and can 194 contribute significantly toward observed non-closure of the Pacific-North America plate circuit. 195 Moreover, the correlation between the distribution of earthquakes and predicted strain or 196 moment rate supports that thermal strain rates are real and released seismically, at least partly. 197 We conclude that horizontal thermal contraction should be considered in future development of 198 the plate tectonic theory. 199 ACKNOWLEDGMENTS We thank G. Blewitt for his help with the GPS data processing. This work was supported by NSF grants OCE (C.K) and OCE (R.G.) 202 REFERENCES CITED 203 Argus, D.F., and Gordon, R.G., 1996, Tests of the rigid-plate hypothesis and bounds on 204 intraplate deformation using geodetic data from very long baseline interferometry: Journal Page 9 of 14

10 Publisher: GSA of Geophysical Research. Solid Earth, v. 101, no. B6, p , doi: /95jb Argus, D.F., Gordon, R.G., Heflin, M.B., Ma, C., Eanes, R.J., Willis, P., Peltier, W.R., and Owen, S.E., 2010, The angular velocities of the plates and the velocity of Earth s centre from space geodesy: Geophysical Journal International, v. 180, no. 3, p , doi: /j x x. 211 Beavan, J., Tregoning, P., Bevis, M., Kato, T., and Meertens, C., 2002, Motion and rigidity of the Pacific Plate and implications for plate boundary deformation: Journal of Geophysical Research. Solid Earth. v. 107, no. B10, p. 2261, doi: /2001jb Bird, P., 2003, An updated digital model of plate boundaries: Geochemistry Geophysics 215 Geosystems, v. 4, no. 3, doi: /2001gc DeMets, C., Gordon, R.G., Argus, D.F., and Stein, S., 1990, Current plate motions: Geophysical 217 Journal International, v. 101, no. 2, p , doi: /j x.1990.tb06579.x. 218 DeMets, C., Gordon, R.G., and Argus, D.F., 2010, Geologically current plate motions: Geophysical Journal International, v. 181, no. 1, p. 1 80, doi: /j x x. 221 Dixon, T.H., Mao, A., and Stein, S., 1996, How rigid is the stable interior of the North American 222 Plate?: Geophysical Research Letters, v. 23, no. 21, p , doi: /96gl Engdahl, E.R., van der Hilst, R., and Buland, R., 1998, Global teleseismic earthquake relocation with improved travel times and procedures for depth determination: Bulletin of the Seismological Society of America, v. 88, no. 3, p Page 10 of 14

11 226 Haines, A.J., and Holt, W.E., 1993, A procedure for obtaining the complete horizontal motions within zones of distributed deformation from the inversion of strain rate data: Journal of Geophysical Research, v. 98, no. B7, p , doi: /93jb Hillier, J.K., and Watts, A.B., 2005, Relationship between depth and age in the North Pacific Ocean: Journal of Geophysical Research. Solid Earth. v. 110, no. B2, doi: /2004JB Kagan, Y.Y., 1999, Universality of the seismic moment-frequency relation: Pure and Applied 233 Geophysics, v. 155, no. 2 4, p , doi: /s Kreemer, C., Holt, W.E., and Haines, A.J., 2002, The global moment rate distribution within plate boundary zones, in Stein, S., and Freymueller, J.T., eds., Plate Boundary Zones, Geodynamics Series 30: Washington D.C., American Geophysical Union, p Kumar, R.R., and Gordon, R.G., 2009, Horizontal thermal contraction of oceanic lithosphere: The ultimate limit to the rigid plate approximation: Journal of Geophysical Research. Solid Earth. v. 114, no. B1, p. B01403, doi: /2007jb Martinod, J., and Molnar, P., 1995, Lithospheric folding in the Indian Ocean and the rheology of 241 the oceanic plate: Bulletin de la Société Géologique de France, v. 166, no. 6, p McKenzie, D.P., 1972, Plate tectonics, in Robertson, E.D. ed., The Nature of the Solid Earth, McGraw-Hill, New York, p McKenzie, D., Jackson, J., and Priestley, K., 2005, Thermal structure of oceanic and continental lithosphere: Earth and Planetary Science Letters, v. 233, no. 3 4, p , doi: /j.epsl Molnar, P., 1979, Earthquake recurrence intervals and plate tectonics: Bulletin of the 246 Seismological Society of America, v. 69, no. 1, p Page 11 of 14

12 247 Müller, R.D., Roest, W.R., Royer, J.-Y., Gahagan, L.M., and Sclater, J.G., 1997, Digital isochrons of the world s ocean floor: Journal of Geophysical Research. Solid Earth. v. 102, no. B2, p , doi: /96jb Okal, E.A., and Sweet, J.R., 2007, Frequency-size distributions for intraplate earthquakes in Stein, S., and Mazzotti, S., eds., Continental Intraplate Earthquakes: Science, Hazard, and Policy Issues: Geological Society of America Special Papers, v. 425, p , doi: / (05). 254 Parmentier, E.M., and Haxby, W.F., 1986, Thermal stresses in the oceanic lithosphere: Evidence from geoid anomalies at fracture zones: Journal of Geophysical Research. Solid Earth. v. 91, no. B7, p , doi: /jb091ib07p Plattner, C., Malservisi, R., Dixon, T.H., LaFemina, P., Sella, G.F., Fletcher, J., and Suarez Vidal, F., 2007, New constraints on relative motion between the Pacific Plate and Baja California microplate (Mexico) from GPS measurements: Geophysical Journal International, v. 170, no. 3, p , doi: /j x x. 261 Sandwell, D., and Fialko, Y., 2004, Warping and cracking of the Pacific plate by thermal 262 contraction: Journal of Geophysical Research, v. 109, no. B10, doi: /2004jb Turcotte, D.L., 1974, Membrane tectonics: Geophysical Journal of the Royal Astronomical Society, v. 36, p Turcotte, D.L., and Oxburgh, E.R., 1967, Finite amplitude convective cells and continental drift: 264 Journal of Fluid Mechanics, v. 28, no. 01, p , doi: /s Wessel, P., 1992, Thermal stresses and the bimodal distribution of elastic thickness estimates of the oceanic lithosphere: Journal of Geophysical Research. Solid Earth. v. 97, no. B10, p , doi: /92jb Page 12 of 14

13 268 Wiens, D.A., and Stein, S., 1983, Age dependence of oceanic intraplate seismicity and implications for lithospheric evolution: Journal of Geophysical Research. Solid Earth. v. 88, no. B8, p , doi: /jb088ib08p FIGURE CAPTIONS 272 Figure 1. A) Contours of log second invariant of model strain rate tensor for Model 1 for which 273 areal strain rates best match the expected values. Linear strain rates saturate at yr -1. White 274 circles are epicenters of selected Pacific intraplate earthquakes from 1960 to 2008 (Engdahl et 275 al., 1998) (see Electronic Supplement). Orthogonal bars indicate the orientations of principal 276 strain rate directions with the lengths of the bars indicating the relative magnitudes of the two 277 horizontal principal strain rates, black if contractional and white if extensional. B) same as A but 278 for Model 2 for which the strain rates best satisfy isotropy. C) Residual GPS velocities (white 279 vectors), after removal of rigid-body rotation, with 95% confidence error ellipses. Black vectors 280 and contours are predicted velocities from thermal contraction (Model 2) are shown in the same 281 frame as GPS, D) Predicted velocities (vectors and contours) from thermal contraction (Model 2) 282 relative to the 0.78 Ma isochron along the Pacific-Antarctic Ridge. 283 Figure 2. A) Normalized cumulative number of earthquakes from oldest to youngest (i.e., 5 Ma 284 old) lithosphere. Also shown are normalized cumulative moment rate for both end-member 2µV [ ( ε models. Moment rate is defined as: xx + ε yy )/2 + [( ε xx ε yy )/2] ε xy 2], with the 286 shear modulus, μ, set to 30 GPa, and volume, V, is the area times a thickness set to the depth of 287 the 700ºC isotherm (or is alternatively limited to be no more 40 km.). B) same as A, but only for 288 lithosphere between 5 and 30 Ma. old. Page 13 of 14

14 289 1 GSA Data Repository item 2014xxx, [Details on GPS data analysis and earthquake catalog], is 290 available online at or on request from 291 editing@geosociety.org or Documents Secretary, GSA, P.O. Box 9140, Boulder, CO 80301, 292 USA. Page 14 of 14